Analytical treatment 1 Article 1 COVID-19 1 Communicable Disease Control 1 Delayed differential equations 1 Disease control 1 Epidemics 1 Harmful effects 1 Humans 1 Italy 1 Linear-chain trick 1 Low dimensional 1 Mass vaccination 1 Multi-phasic age-structured epidemics Non-pharmaceutical interventions 1 Ordinary differential equations 1 Pandemics 1 Piece-wise constants 1 SARS-CoV-2 1 SIR epidemic model 1 Social distancing 1 Stable age distributions 1 Transient dynamics 1 aging 1 analytic method 1 communicable disease control 1 coronavirus disease 2019 1 disease incidence 1 epidemic 1 epidemiology 1